Generalized Quantifiers

Abstract

In Part I of this book it was argued that natural language quantifies over possible worlds. But I can imagine that there may be those who will say that all that has been shewn is that sentential operators can mimic quantification, and not that they amount to genuine quantification. Equivalence proofs, they will rightly point out, do go both ways, and so Part I could equally be taken to shew that the apparent quantification over worlds is not genuine. My own attitude, as expressed in various places in Part I, is that “quantification is as quantification does”, but the present part of the book is designed to provide a stronger argument for the conclusion of Part I. In this part of the book I shall shew that ordinary quantification over individuals can also be given an indexical treatment using sentential operators. So if Part I can be used to shew that natural language does not quantify over possible worlds then Part III can be used to shew that it does not quantify over anything.